In Corollary REF , it follows of course that, if \(H\)  can be both attached to \(\mathcal {A}\)  and detached from \(\mathcal {A}\)  then
\(\; |\rm pend(R_n,H)/n\: - \alpha | < \varepsilon \)  wvhp; and thus \(\rm pend(R_n,H)/n \rightarrow \alpha \)  in probability as \(n \rightarrow \infty \) .
In the special case when \(\mathcal {A}\)  is the class \(\mathcal {E}^S\)  of graphs embeddable in a given surface \(S\) , it is known further that \(\rm pend(R_n,H)\)  is asymptotically normally distributed
[1]}, [2]}.
